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| Preface | |
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| Introduction and Review | |
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| Some Notation and Terminology | |
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| Matrix Arithmetic | |
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| Inner Products and Orthogonality | |
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| Determinants | |
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| Vector Spaces | |
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| Definitions and Examples | |
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| Subspaces | |
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| Linear Independence | |
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| Sums and Intersections of Subspaces | |
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| Linear Transformations | |
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| Definition and Examples | |
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| Matrix Representation of Linear Transformations | |
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| Composition of Transformations | |
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| Structure of Linear Transformations | |
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| Four Fundamental Subspaces | |
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| Introduction to the Moore-Penrose Pseudoinverse | |
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| Definitions and Characterizations | |
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| Examples | |
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| Properties and Applications | |
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| Introduction to the Singular Value Decomposition | |
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| The Fundamental Theorem | |
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| Some Basic Properties | |
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| Row and Column Compressions | |
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| Linear Equations | |
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| Vector Linear Equations | |
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| Matrix Linear Equations | |
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| A More General Matrix Linear Equation | |
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| Some Useful and Interesting Inverses | |
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| Projections, Inner Product Spaces, and Norms | |
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| Projections | |
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| The four fundamental orthogonal projections | |
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| Inner Product Spaces | |
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| Vector Norms | |
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| Matrix Norms | |
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| Linear Least Squares Problems | |
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| The Linear Least Squares Problem | |
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| Geometric Solution | |
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| Linear Regression and Other Linear Least Squares Problems | |
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| Example: Linear regression | |
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| Other least squares problems | |
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| Least Squares and Singular Value Decomposition | |
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| Least Squares and QR Factorization | |
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| Eigenvalues and Eigenvectors | |
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| Fundamental Definitions and Properties | |
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| Jordan Canonical Form | |
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| Determination of the JCF | |
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| Theoretical computation | |
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| On the +1's in JCF blocks | |
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| Geometric Aspects of the JCF | |
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| The Matrix Sign Function | |
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| Canonical Forms | |
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| Some Basic Canonical Forms | |
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| Definite Matrices | |
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| Equivalence Transformations and Congruence | |
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| Block matrices and definiteness | |
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| Rational Canonical Form | |
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| Linear Differential and Difference Equations | |
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| Differential Equations | |
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| Properties of the matrix exponential | |
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| Homogeneous linear differential equations | |
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| Inhomogeneous linear differential equations | |
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| Linear matrix differential equations | |
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| Modal decompositions | |
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| Computation of the matrix exponential | |
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| Difference Equations | |
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| Homogeneous linear difference equations | |
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| Inhomogeneous linear difference equations | |
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| Computation of matrix powers | |
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| Higher-Order Equations | |
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| Generalized Eigenvalue Problems | |
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| The Generalized Eigenvalue/Eigenvector Problem | |
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| Canonical Forms | |
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| Application to the Computation of System Zeros | |
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| Symmetric Generalized Eigenvalue Problems | |
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| Simultaneous Diagonalization | |
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| Simultaneous diagonalization via SVD | |
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| Higher-Order Eigenvalue Problems | |
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| Conversion to first-order form | |
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| Kronecker Products | |
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| Definition and Examples | |
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| Properties of the Kronecker Product | |
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| Application to Sylvester and Lyapunov Equations | |
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| Bibliography | |
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| Index | |